Y. Sumino

Static QCD potential at three-loop order.

We compute the purely gluonic contribution to the static QCD potential at three-loop order. This completes computation of the static potential at this order.

Violation of Casimir Scaling for Static QCD Potential at Three-loop Order

We compute the full O(� 4 ) and O(� 4 logs) corrections to the potential VR(r) between the static color sources, where VR(r) is defined from the Wilson loop in a general representation R of a general gauge group G. We find a violation of the Casimir scaling of the potential, for the first time, at O(� 4 ). The effect of the Casimir scaling violation is predicted to reduce the tangent of VR(r)/CR proportionally to specific color factors dependent on R. We study the sizes of the Casimir scaling violation for various Rs in the case G = SU(3). We find that they are well within the present bounds from lattice calculations, in the distance region where both perturbative and lattice computations of VR(r) are valid. We also discuss how to test the Casimir scaling violating effect.

Family gauge symmetry and Koide's mass formula

Abstract Koides mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We propose a mechanism for cancelling the QED correction to Koides formula. This is discussed in an effective theory with U ( 3 ) family gauge symmetry and a scenario in which this symmetry is unified with SU ( 2 ) L symmetry at 10 2 – 10 3 TeV scale.

Weight function method for precise determination of top quark mass at Large Hadron Collider

Abstract We propose a new method to measure a theoretically well-defined top quark mass at the LHC. This method is based on the “weight function method,” which we proposed in our preceding paper. It requires only lepton energy distribution and is basically independent of the production process of the top quark. We perform a simulation analysis of the top quark mass reconstruction with t t ¯ pair production and lepton + jets decay channel at the leading order. The estimated statistical error of the top quark mass is about 0.4 GeV with an integrated luminosity of 100 fb − 1 at s = 14 TeV . We also estimate some of the major systematic uncertainties and find that they are under good control.

Family Gauge Symmetry as an Origin of Koide's Mass Formula and Charged Lepton Spectrum

Koides mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We present a model of charged lepton sector within an effective field theory with U(3) × SU(2) family gauge symmetry, which predicts Koides formula within the present experimental accuracy. Radiative corrections as well as other corrections to Koides mass formula have been taken into account. We adopt a known mechanism, through which the charged lepton spectrum is determined by the vacuum expectation value of a 9-component scalar field Φ. On the basis of this mechanism, we implement the following mechanisms into our model: (1) The radiative correction induced by family gauge interaction cancels the QED radiative correction to Koides mass formula, assuming a scenario in which the U(3) family gauge symmetry and SU(2)L weak gauge symmetry are unified at 102–103 TeV scale; (2) A simple potential of Φ invariant under U(3) × SU(2) leads to a realistic charged lepton spectrum, consistent with the experimental values, assuming that Koides formula is protected; (3) Koides formula is stabilized by embedding U(3) × SU(2) symmetry in a larger symmetry group. Formally fine tuning of parameters in the model is circumvented (apart from two exceptions) by appropriately connecting the charged lepton spectrum to the boundary (initial) conditions of the model at the cut-off scale. We also disucss some phenomenological implications.

A scale-invariant Higgs sector and structure of the vacuum

A bstractIn view of the current status of measured Higgs boson properties, we consider a question whether only the Higgs self-interactions can deviate significantly from the Standard-Model (SM) predictions. This may be possible if the Higgs effective potential is irregular at the origin. As an example we investigate an extended Higgs sector with singlet scalar(s) and classical scale invariance. We develop a perturbative formulation necessary to analyze this model in detail. The behavior of a phenomenologically valid potential in the perturbative regime is studied around the electroweak scale. We reproduce known results: the Higgs self-interactions are substantially stronger than the SM predictions, while the Higgs interactions with other SM particles are barely changed. We further predict that the interactions of singlet scalar(s), which is a few to several times heavier than the Higgs boson, tend to be fairly strong. If probed, these features will provide vivid clues to the structure of the vacuum. We also examine Veltman’s condition for the Higgs boson mass.

Algorithms to Evaluate Multiple Sums for Loop Computations

We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hyper-geometric-type sums, ∑n1,⋯,nNΓ(a1·n+c1)Γ(a2·n+c2)⋯Γ(aP·n+cP)Γ(b1·n+d1)Γ(b2·n+d2)⋯Γ(bQ·n+dQ)x1n1⋯xNnN with ai·n=∑j=1Naijnj, etc., in a small parameter e around rational values of ci,di’s. Type I sum corresponds to the case where, in the limit e → 0, the summand reduces to a rational function of nj’s times x1n1⋯xNnN; ci,di’s can depend on an external integer index. Type II sum is a double sum (N = 2), where ci, di’s are half-integers or integers as e → 0 and xi = 1; we consider some specific cases where at most six Γ functions remain in the limit e → 0. The algorithms enable evaluations of arbitrary expansion coefficients in e in terms of Z-sums and multiple polylogarithms (generalized multiple zeta values). We also present applications of these algorithms. In particular, Type I sums can be used to generate a new class of relations among generalized mult...

Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order

Abstract We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers n , l , s and j , up to O ( α s 5 m ) and O ( α s 5 m log ⁡ α s ) in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers ( π , ζ ( 3 ) , ζ ( 5 ) ) and finite sums (besides the 3-loop constant a ¯ 3 of the static potential whose full analytic form is still unknown). A derivation of the formula is given.

Boost-invariant leptonic observables and reconstruction of parent particle mass

Abstract We propose a class of observables constructed from lepton energy distribution, which are independent of the velocity of the parent particle if it is scalar or unpolarized. These observables may be used to measure properties of various particles in the LHC experiments. We demonstrate their usage in a determination of the Higgs boson mass.

Strong IR cancellation in heavy quarkonium and precise top mass determination

A bstractCombining recent perturbative analyses on the static QCD potential and the quark pole mass, we find that, for the heavy quarkonium states cc¯